Coreless power transformer

A method of implementing energy transfer comprising:

• producing magnetic fields using a drive coil;
• providing a load coil;
• magnetically coupling a first resonant coil of length X2 to the drive coil producing energy that is stored by the first resonant coil;
• and
• magnetically coupling a second resonant coil of length X2 to the first resonant coil to propagate the energy stored in the first resonant coil to the second resonant coil without using a magnetic core, the second resonant coil is then magnetically coupled to the load coil where the energy is transferred to the load coil, wherein the drive coil, the load coil, the first resonant coil, and
• the second resonant coil form four magnetically coupled coils having fixed spacing geometry, and a first scaling parameter f1 is used to characterize a first variation position where the drive coil is wrapped around the first resonant coil, and a second scaling parameter f2 is used to characterize a second variation position where the load coil is wrapped around the second resonant coil, the first scaling parameter f1 and the second scaling parameter f2 are defined as:
• fi=d1/X2 and f2=d2/X2, where d1 represents a first distance between a first center position of the drive coil and a first edge of the first resonant coil and d2 represents
• a second distance between a second center position of the load coil and a second edge of the second resonant coil and
• picking any of or a combination of a group of parameters are picked to achieve a pre-defined transmission coefficient, and the group of parameters are the first center position, the second center position, a separation distance between the first resonant coil and the second resonant coil, a number of turns in the first resonant coil, a number of turns in the second resonant coil, a number of turns in the drive coil, and a number of turns in the load coil.

A coreless transformer comprising:

• four magnetically coupled coils having fixed spacing geometry comprising:
• a drive coil that produces magnetic fields;
• a load coil;
• a first resonant coil of length X2 that is magnetically coupled to the drive coil producing energy that is stored by the first resonant coil;
• a second resonant coil of length X2 that is magnetically coupled to the first resonant coil to propagate the energy stored in the first resonant coil to the second resonant coil without using a magnetic core, wherein the second resonant coil is then magnetically coupled to the load coil where the energy is transferred to the load coil and
• wherein at least a portion of the first resonant coil is nested under the drive coil and at least a portion of the second resonant coil is nested under the load coil
• wherein a first scaling parameter f1 is used to characterize a first variation position where the drive coil is wrapped around the first resonant coil, and a second scaling parameter f2 is used to characterize a second variation position where the load coil is wrapped around the second resonant coil, and the first scaling parameter f1 and the second scaling parameter f2 are defined as:
• fi=d1/X2 and f2=d2/X2, where d1 represents a first distance between a first center position of the drive coil and a first edge of the first resonant coil and d2 represents a second distance between a second center position of the load coil and a second edge of the second resonant coil, and
• wherein any of or a combination of a group of parameters are picked to achieve a pre-defined transmission coefficient, and the group of parameters are the first center position, the second center position, a separation distance between the first resonant coil and the second resonant coif a number of turns in the first resonant coif a number of turns in the second resonant coif a number of turns in the drive coif and a number of turns in the load coil.